Answer:
[tex]Area\ of\ whole\ figure\ = 49.12 ft^2\\[/tex]
Step-by-step explanation:
If we see closely the figure consists of right angled triangle and a semi-circle, so area of the whole figure would be Area of the triangle + Area of the semi-circle so here goes,
We calculate firstly the Area of the triangle,
[tex]Area\ of\ triangle\ =\frac{1}{2}*b*h\\\\Area\ of\ triangle\ =\frac{1}{2}*6*8\\\\Area\ of\ triangle\ =24\ ft^{2} \\[/tex]
Now we calculate the area of the semi-circle,
Semi-circle is also called as Half of a circle, so,
[tex]Area\ of\ a\ circle\ = \pi r^2[/tex]
then area of half a circle would be,
[tex]Area\ of\ a\ semi\ circle\ = \frac{\pi r^2 }{2} \\[/tex]
where r is the radius of the circle,
but we don't have the radius we have the diameter which is 8ft to find out the value of radius we divide the diameter by 2 , the formula is:
[tex]d=2r[/tex]
where d is the diameter and r is the radius of the circle, so,
[tex]d=2r\\8=2r\\8/2=r\\4=r\\[/tex]
so now we insert the value of radius which is 4ft into the area of a semi-circle,
[tex]Area\ of\ a\ semi\ circle\ = \frac{\pi r^2 }{2} \\\\Area\ of\ a\ semi\ circle\ = \frac{\pi (4)^2 }{2} \\\\Area\ of\ a\ semi\ circle\ = \frac{16\pi }{2} \\\\Area\ of\ a\ semi\ circle\ = 25.12\ ft^2\\[/tex]
Now the Area of the whole figure is
Area of Whole figure = Area of half a circle + Area of triangle
Area of whole figure = 25.12 + 24
Area of whole figure = 49.12 ft^2
